In this work, the Benjamin-Bona-Mahoney-Burgers equation is examined which includes the dual power law nonlinearity and diffraction term. The exact solutions of governing equation are obtained by exploting the modified exp-function method. For some specific values of constants, the obtained travelling wave soluions are dark soliton, periodic and singular in nature. Also, 3-D, 2-D and contour graphical representations of obtained solutions are displayed.
{"title":"Exact Solutions of Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-Law Nonlinearity by Modified Exp-Function Method","authors":"Manjeet Sharma, Rajesh Kumar Gupta","doi":"10.37256/cm.5120232434","DOIUrl":"https://doi.org/10.37256/cm.5120232434","url":null,"abstract":"In this work, the Benjamin-Bona-Mahoney-Burgers equation is examined which includes the dual power law nonlinearity and diffraction term. The exact solutions of governing equation are obtained by exploting the modified exp-function method. For some specific values of constants, the obtained travelling wave soluions are dark soliton, periodic and singular in nature. Also, 3-D, 2-D and contour graphical representations of obtained solutions are displayed.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135149231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, the Benjamin-Bona-Mahoney-Burgers equation is examined which includes the dual power law nonlinearity and diffraction term. The exact solutions of governing equation are obtained by exploting the modified exp-function method. For some specific values of constants, the obtained travelling wave soluions are dark soliton, periodic and singular in nature. Also, 3-D, 2-D and contour graphical representations of obtained solutions are displayed.
{"title":"Exact Solutions of Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-Law Nonlinearity by Modified Exp-Function Method","authors":"Manjeet Sharma, Rajesh Kumar Gupta","doi":"10.37256/cm.4420232434","DOIUrl":"https://doi.org/10.37256/cm.4420232434","url":null,"abstract":"In this work, the Benjamin-Bona-Mahoney-Burgers equation is examined which includes the dual power law nonlinearity and diffraction term. The exact solutions of governing equation are obtained by exploting the modified exp-function method. For some specific values of constants, the obtained travelling wave soluions are dark soliton, periodic and singular in nature. Also, 3-D, 2-D and contour graphical representations of obtained solutions are displayed.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"138 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135045842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The primary purpose of this paper is to investigate and recover implicit quiescent optical solitons in the context of the dispersive concatenation model in nonlinear optics. Specifically, the study focuses on a model that incorporates nonlinear chromatic dispersion and includes Kerr and power-law self-phase modulation effects. The objective is to identify and characterize these soliton solutions within this complex optical system. To achieve this purpose, we employ the Lie symmetry analysis method. Lie symmetry analysis is a powerful mathematical technique commonly used in physics and engineering to identify symmetries and invariance properties of differential equations. In this context, it is used to uncover the underlying symmetries of the nonlinear optical model, which in turn aids in the recovery of the quiescent optical solitons. This method involves mathematical derivations and calculations to determine the solutions. The outcomes of the current paper include the successful recovery of implicit quiescent optical solitons for the dispersive concatenation model with nonlinear chromatic dispersion, Kerr, and power-law self-phase modulation. The study provides mathematical expressions and constraints on the model’s parameters that yield upper and lower bounds for these solutions. Essentially, this paper presents a set of mathematical descriptions for the optical solitons that can exist within the described optical system. The present paper contributes to the field of nonlinear optics by exploring the behavior of optical solitons in a model that combines multiple nonlinear effects. This extends our understanding of complex optical systems.
{"title":"Implicit Quiescent Optical Solitons for the Dispersive Concatenation Model with Nonlinear Chromatic Dispersion by Lie Symmetry","authors":"Abdullahi Rashid Adem, Anjan Biswas, Yakup Yildirim, Asim Asiri","doi":"10.37256/cm.4420233575","DOIUrl":"https://doi.org/10.37256/cm.4420233575","url":null,"abstract":"The primary purpose of this paper is to investigate and recover implicit quiescent optical solitons in the context of the dispersive concatenation model in nonlinear optics. Specifically, the study focuses on a model that incorporates nonlinear chromatic dispersion and includes Kerr and power-law self-phase modulation effects. The objective is to identify and characterize these soliton solutions within this complex optical system. To achieve this purpose, we employ the Lie symmetry analysis method. Lie symmetry analysis is a powerful mathematical technique commonly used in physics and engineering to identify symmetries and invariance properties of differential equations. In this context, it is used to uncover the underlying symmetries of the nonlinear optical model, which in turn aids in the recovery of the quiescent optical solitons. This method involves mathematical derivations and calculations to determine the solutions. The outcomes of the current paper include the successful recovery of implicit quiescent optical solitons for the dispersive concatenation model with nonlinear chromatic dispersion, Kerr, and power-law self-phase modulation. The study provides mathematical expressions and constraints on the model’s parameters that yield upper and lower bounds for these solutions. Essentially, this paper presents a set of mathematical descriptions for the optical solitons that can exist within the described optical system. The present paper contributes to the field of nonlinear optics by exploring the behavior of optical solitons in a model that combines multiple nonlinear effects. This extends our understanding of complex optical systems.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135045086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Magdy, W. M. Abd-Elhameed, Y. H. Youssri, G. M. Moatimid, A. G. Atta
This paper presents a numerical strategy for solving the nonlinear time fractional Burgers's equation (TFBE) to obtain approximate solutions of TFBE. During this procedure, the collocation approach is used. The proposed numerical approximations are supposed to be a double sum of the products of two sets of basis functions. The two sets of polynomials are presented here: a modified set of shifted Gegenbauer polynomials and a shifted Gegenbauer polynomial set. Some specific integers and fractional derivatives are explicitly given as a combination of basis functions to apply the proposed collocation procedure. This method transforms the governing boundary-value problem into a set of nonlinear algebraic equations. Newton's approach can be used to solve the resulting nonlinear system. An analysis of the precision of the proposed method is provided. Various examples are presented and compared to some existing methods in the literature to prove the reliability of the suggested approach.
{"title":"A Potent Collocation Approach Based on Shifted Gegenbauer Polynomials for Nonlinear Time Fractional Burgers’ Equations","authors":"E. Magdy, W. M. Abd-Elhameed, Y. H. Youssri, G. M. Moatimid, A. G. Atta","doi":"10.37256/cm.4420233302","DOIUrl":"https://doi.org/10.37256/cm.4420233302","url":null,"abstract":"This paper presents a numerical strategy for solving the nonlinear time fractional Burgers's equation (TFBE) to obtain approximate solutions of TFBE. During this procedure, the collocation approach is used. The proposed numerical approximations are supposed to be a double sum of the products of two sets of basis functions. The two sets of polynomials are presented here: a modified set of shifted Gegenbauer polynomials and a shifted Gegenbauer polynomial set. Some specific integers and fractional derivatives are explicitly given as a combination of basis functions to apply the proposed collocation procedure. This method transforms the governing boundary-value problem into a set of nonlinear algebraic equations. Newton's approach can be used to solve the resulting nonlinear system. An analysis of the precision of the proposed method is provided. Various examples are presented and compared to some existing methods in the literature to prove the reliability of the suggested approach.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135253426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The principal aim of the present work is to investigate a new class of integral transforms involving the product of Bessel function of the first kind of arbitrary order with generalized Laguerre polynomials and logarithmic functions which deduce some new results in terms of the digamma function and Kamp´e de F´eriet functions. A novel expression is found for the Kamp´e de F´eriet function F1:2;1 2:1;0 in terms of hypergeometric functions 1F1, 2F2 and 3F2. Finally, The results obtained are applied in the problem of propagation of Laguerre-Bessel-Gaussian Schell-model beams as an application.
本文的主要目的是研究一类新的积分变换，它涉及第一类任意阶贝塞尔函数与广义拉盖尔多项式和对数函数的乘积，用二格玛函数和Kamp ' e de F ' eriet函数推导出一些新的结果。在超几何函数1F1, 2F2和3F2中发现了Kamp ' e de F ' eriet函数F1:2;1 2:1;0的新表达式。最后，将所得结果应用于拉盖尔-贝塞尔-高斯-谢尔模型光束的传播问题。
{"title":"Certain Integral Transforms and Their Applications in Propagation of Laguerre-Gaussian Schell-model Beams","authors":"Abdelmajid Belafhal, E. M. El Halba, Talha Usman","doi":"10.37256/cm.4420232421","DOIUrl":"https://doi.org/10.37256/cm.4420232421","url":null,"abstract":"The principal aim of the present work is to investigate a new class of integral transforms involving the product of Bessel function of the first kind of arbitrary order with generalized Laguerre polynomials and logarithmic functions which deduce some new results in terms of the digamma function and Kamp´e de F´eriet functions. A novel expression is found for the Kamp´e de F´eriet function F1:2;1 2:1;0 in terms of hypergeometric functions 1F1, 2F2 and 3F2. Finally, The results obtained are applied in the problem of propagation of Laguerre-Bessel-Gaussian Schell-model beams as an application.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134960444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, for the Omicron Variant, a mathematical model of epidemic SQIRV fractional order is constructed. This model's positivity and boundedness have been investigated and confirmed. In the sense of the Caputo derivative, this model's existence and uniqueness are investigated. The reproduction number $R_0$, which is used to determine whether or not the disease would spread further, is calculated to demonstrate that infection steady-state solutions are asymptotically stable. Different orders of fractional derivatives are used to explore the numerical simulations.
{"title":"Fractional Order SQIRV Mathematical Model for Omicron Variant in the Caputo Sense","authors":"Pushpendra Kumar, S. Dickson, S. Padmasekaran","doi":"10.37256/cm.4420232373","DOIUrl":"https://doi.org/10.37256/cm.4420232373","url":null,"abstract":"In this paper, for the Omicron Variant, a mathematical model of epidemic SQIRV fractional order is constructed. This model's positivity and boundedness have been investigated and confirmed. In the sense of the Caputo derivative, this model's existence and uniqueness are investigated. The reproduction number $R_0$, which is used to determine whether or not the disease would spread further, is calculated to demonstrate that infection steady-state solutions are asymptotically stable. Different orders of fractional derivatives are used to explore the numerical simulations.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135817044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
None Renu, None Sarita, Amit Sehgal, None Archana Malik
The prime index graph π(G) of a finite group G is a special type of undirected simple graph whose vertex set is set of subgroups of G, in which two distinct vertices are adjacent if one has prime index in the other. Let p and q be distinct primes. In this paper, we establish that prime index graph of a finite cyclic p-group Zpn, a finite abelian group Zpn × Zq and a finite abelian p-group Zp × Zpn always have graceful labeling without any condition on n using the concept of path graph or p-layer ladder graph of size n + 1.
{"title":"Graceful Labeling of Prime Index Graph of Group Zp × Zpn","authors":"None Renu, None Sarita, Amit Sehgal, None Archana Malik","doi":"10.37256/cm.4320232727","DOIUrl":"https://doi.org/10.37256/cm.4320232727","url":null,"abstract":"The prime index graph π(G) of a finite group G is a special type of undirected simple graph whose vertex set is set of subgroups of G, in which two distinct vertices are adjacent if one has prime index in the other. Let p and q be distinct primes. In this paper, we establish that prime index graph of a finite cyclic p-group Zpn, a finite abelian group Zpn × Zq and a finite abelian p-group Zp × Zpn always have graceful labeling without any condition on n using the concept of path graph or p-layer ladder graph of size n + 1.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135153736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elsayed M. E. Zayed, Khaled A. Gepreel, Mahmoud El-Horbaty, Anjan Biswas, Yakup Yildirim, Houria Triki, Asim Asiri
The study undertakes a comprehensive exploration of optical solitons within the context of the dispersive concatenation model, utilizing three distinct integration algorithms. These approaches, namely the enhanced Kudryashov' s method, the Riccati equation expansion approach, and the Weierstrass' expansion scheme, offer distinct perspectives and insights into the behavior of optical solitons. By employing the enhanced Kudryashov' s approach, the research uncovers a spectrum of soliton solutions, including straddled, bright, and singular optical solitons. This algorithm not only provides a nuanced understanding of the various soliton types but also highlights the occurrence of singular solitons that exhibit unique characteristics. The Riccati equation expansion approach, on the other hand, yields dark solitons in addition to singular solitons. This particular method expands our comprehension of soliton behavior by encompassing the presence of dark solitons alongside singular ones. This diversification contributes to a more comprehensive grasp of soliton phenomena. Furthermore, the application of the Weierstrass' expansion scheme extends the analysis to encompass bright, singular, and other variations of straddled solitons. This method introduces further complexity and diversity to the optical soliton. Importantly, the study meticulously addresses the parameter constraints that govern the behavior of these solitons. By providing a comprehensive presentation of these constraints, the research enhances the practical applicability of the findings, offering insights into the conditions under which these soliton solutions emerge.
{"title":"Optical Solitons for the Dispersive Concatenation Model","authors":"Elsayed M. E. Zayed, Khaled A. Gepreel, Mahmoud El-Horbaty, Anjan Biswas, Yakup Yildirim, Houria Triki, Asim Asiri","doi":"10.37256/cm.4320233321","DOIUrl":"https://doi.org/10.37256/cm.4320233321","url":null,"abstract":"The study undertakes a comprehensive exploration of optical solitons within the context of the dispersive concatenation model, utilizing three distinct integration algorithms. These approaches, namely the enhanced Kudryashov' s method, the Riccati equation expansion approach, and the Weierstrass' expansion scheme, offer distinct perspectives and insights into the behavior of optical solitons. By employing the enhanced Kudryashov' s approach, the research uncovers a spectrum of soliton solutions, including straddled, bright, and singular optical solitons. This algorithm not only provides a nuanced understanding of the various soliton types but also highlights the occurrence of singular solitons that exhibit unique characteristics. The Riccati equation expansion approach, on the other hand, yields dark solitons in addition to singular solitons. This particular method expands our comprehension of soliton behavior by encompassing the presence of dark solitons alongside singular ones. This diversification contributes to a more comprehensive grasp of soliton phenomena. Furthermore, the application of the Weierstrass' expansion scheme extends the analysis to encompass bright, singular, and other variations of straddled solitons. This method introduces further complexity and diversity to the optical soliton. Importantly, the study meticulously addresses the parameter constraints that govern the behavior of these solitons. By providing a comprehensive presentation of these constraints, the research enhances the practical applicability of the findings, offering insights into the conditions under which these soliton solutions emerge.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135938495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Balaji R, Antline Nisha B, Saradha M, R. Udhayakumar
We aimed to solve first-order differential equations using two novel techniques: the harmonic mean and the cubic mean of Euler' s modified approach for fuzzy primary value in this research proposal. We present a new formulation of Euler' s classic approach based on Zadeh' s extension concept to address this dependency issue in a fuzzy situation. In the literature, numerical approaches for solving differential equations with fuzzy main values often disregard this issue. With a few examples, we show how our approach outperforms more traditional fuzzy approaches based on Euler' s method.
{"title":"Numerical Solutions of Fuzzy Differential Equations by Harmonic Mean and Cubic Mean of Modified Euler' s Method","authors":"Balaji R, Antline Nisha B, Saradha M, R. Udhayakumar","doi":"10.37256/cm.4320233393","DOIUrl":"https://doi.org/10.37256/cm.4320233393","url":null,"abstract":"We aimed to solve first-order differential equations using two novel techniques: the harmonic mean and the cubic mean of Euler' s modified approach for fuzzy primary value in this research proposal. We present a new formulation of Euler' s classic approach based on Zadeh' s extension concept to address this dependency issue in a fuzzy situation. In the literature, numerical approaches for solving differential equations with fuzzy main values often disregard this issue. With a few examples, we show how our approach outperforms more traditional fuzzy approaches based on Euler' s method.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136299162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Diverse World of PDEs","authors":"","doi":"10.1090/conm/789","DOIUrl":"https://doi.org/10.1090/conm/789","url":null,"abstract":"","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135840631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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